In this research project, the researcher carried out the program to study a correspondence between Galois representations (in the algebraic side) and automorphic forms (in the analytic side). Usually we understand it via p-adic Galois representations and it's reduction which is often called mod p representation. Then we have to divide the modularity problem into the type of mod p representation in question and plug them into the full modularity problem.In this project He studied the property of modular mod p representation so that any such representation could be reduced to a manageable class of mod p representation.